Question: Simplify the following expression: $y = \dfrac{5p^2 - 15p - 270}{p - 9} $
Explanation: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $5$ , so we can rewrite the expression: $ y =\dfrac{5(p^2 - 3p - 54)}{p - 9} $ Then we factor the remaining polynomial: $p^2 {-3}p {-54} $ ${-9} + {6} = {-3}$ ${-9} \times {6} = {-54}$ $ (p {-9}) (p + {6}) $ This gives us a factored expression: $\dfrac{5(p {-9}) (p + {6})}{p - 9}$ We can divide the numerator and denominator by $(p + 9)$ on condition that $p \neq 9$ Therefore $y = 5(p + 6); p \neq 9$